# Multiplying and dividing radicals

### Multiplying and dividing radicals

Before doing any multiplication or division, we need to make sure the indices are the same. Multiplying radicals is simply multiplying the numbers inside the radical sign, the radicands, together. When dividing radicals, you can put both the numerator and denominator inside the same square roots.

#### Lessons

• Introduction
a)
How to simplify radicals?

b)
• What is a radical?
• How to multiply radicals?
• How to divide radicals?
• General rules when we are dealing with variables in radicals

• 1.
Write the following as a single radical = $\sqrt{x}$
a)
$\sqrt{3} \times \sqrt{8}$

b)
$\sqrt{7 \times 11}$

c)
$\sqrt{150} \over \sqrt{15}$

d)
$\frac{( \sqrt{20} \times \sqrt{5})} {\sqrt{64}}$

• 2.
Express the following radicals as a product of radicals
a)
$\sqrt{45}$

b)
- $\sqrt{77}$

• 3.
Multiplying and dividing radicals
a)
-4$\sqrt{2}$ * - $\sqrt{2}$

b)
5$\sqrt{2}$ * 6 $\sqrt{10}$ * 7 $\sqrt{50}$

c)
$\sqrt{3 }$ ( $\sqrt{8} + 4)$

d)
(4 $\sqrt{10 }$ - 3 $\sqrt{6}$ )(5 $\sqrt{2 } - \sqrt{5} )$